Essay on the Interpretation of Milk Records. 163 



Now if the regression is linear, i.e., if the means of arrays 

 fall on the line representing characteristic regression, we shall 

 be justified in using those coefficients for estimating totals from 

 any of the other three figures. 



The following diagram taken from the correlation table 

 already given of totals and revised maxima for 1,233 normal 

 cows represents perhaps the most satisfactory of any of the 

 results obtained. It shows clearly that the regression is very 

 nearly linear. 



Fig. 3. — Eeqeession of Totals relative to Revised Maxima. 

 1,233 Normal Lactations. 



ab Line of Regression. 

 X Mean of Total and R.M. 

 Means of Arrays of 

 Totals. 



Coef. of regression. 



Totals relative to R.M. 

 ■41-54 + 518. 



R.M. relative to Totals 

 0017 -I- -0002. 



With regard to its practical application, take for example 

 the case of a cow giving a revised maximum of ten quarts. 



Since the mean revised maximum is 14 quarts, she differs 

 from that mean by —4 quarts. Her total will therefore differ 

 from the mean of totals, which is 656 gallons, by — (4 x 41*5) 

 gallons ; i.e., her probable normal yield will be 6r)6 — 166 

 gallons == say .500 gallons. Further, the chances are even that 

 this estimate of 500 gallons is correct within the limits of ± 60 

 gallons. ^ 



' P.E. of estimate = 0-6745 X <t \/ 1 - ?•'. The factor 0-6745 is not 

 strictly legitimate where distribution is not normal. 



a\2 



